\ A thermodynamic cycle of 1 mole ideal monatomic gas goes through 4 reversible steps\ (A to

D

) as shown in the figure blew. Step

A

(state

1->2

) is adiabatic. Step

B(2->3)

is at\ constant volume. Step

C(3->4)

is adiabatic and

D(4->1)

is at constant volume. Give your\ answer in SI units and 2 decimal places. Hint: use

R

insteod of

k_(B)

since

n=1

mole. (10\ points total)\ The Following are known:

T1=330K,T3=400K,W_(sys )(A)=+374.13J

\ a) For

stepA(1->2)

, the system work

W_(sys)

is given above. What is the temperature of\ state

2,T_(2)

? What is the system

q,\\\\Delta U

and

\\\\Delta S

? (3 pts)\ b) For step

B(2->3)

, what is the system

q,\\\\Delta U

and

\\\\Delta S

?

T_(3)

is given above. Note that

T

is\ not a constant in this step! To derive

\\\\Delta S

, use the definition

\\\\Delta S=\\\\int (dq)/(T)

and

dq=dU

\ for a constant volume process. (4 pts)\ c) What is the change of system entropy

\\\\Delta S

for step

D(4->1)

? What is the system\ temperature at state

4,T_(4)

? (3 pts)

A thermodynamic cycle of 1 mole ideal monatomic gas goes through 4 reversible steps (A to D ) as shown in the figure blew. Step A( state 12 ) is adiabatic. Step B(2>3) is at constant volume. Step C(3>4) is adiabatic and D(4>1) is at constant volume. Give your answer in SI units and 2 decimal places. Hint: use R instead of kE since n=1 mole. (10 points total) The Following are known: T1=330K,T3=400K,Wsys(A)=+374.13J a) For step A(1>2), the system work Wsys is given above. What is the temperature of state 2,T2 ? What is the system q,U and S ? (3 pts) b) For step B(2>3), what is the system q,U and S?T3 is given above. Note that T is not a constant in this step! To derive S, use the definition S=Tdq and dq=dU for a constant volume process. (4 pts) c) What is the change of system entropy S for step D(4>1) ? What is the system temperature at state 4,T4 ? (3 pts)